THE NULL-CONE AND COHOMOLOGY OF VECTOR BUNDLES ON FLAG VARIETIES
Kari Vilonen, Ting Xue
REPRESENTATION THEORY | AMER MATHEMATICAL SOC | Published : 2016
We study the null-cone of a semi-simple algebraic group acting on a number of copies of its Lie algebra via the diagonal adjoint action. We show that the null-cone has rational singularities in the case of SL3. We observe by example that the null-cone is not normal in general and that the normalization of the null-cone does not have rational singularities in general. This is achieved by computing cohomology of certain vector bundles on flag varieties.
Related Projects (2)
Awarded by NSF
Awarded by ARC
The first author was supported in part by NSF grants DMS-1402928 and DMS-1069316, the Academy of Finland, and the ARC grant DP150103525.The second author was supported in part by the ARC grants DP150103525, DE160100975, and the Academy of Finland.